Hardware Reference
In-Depth Information
be concurrently executed. Therefore, from the sequencing graph, we can find that the
maximum number of dilution/mixing operations that can be executed concurrently
is 8. When executing these 8 dilution/mixing operations, the biochip may also
execute another 8 dispensing operations.
From the above analysis, we can find that the maximum degree of parallelism for
fluid-handling operation is: simultaneously implementing 8 mixing operations (and
each mixing operation involves two droplets) and 8 dispensing operations (and each
mixing operation involves one droplet). Therefore, the maximum number of droplets
can be concurrently manipulated on the biochip can be calculated as 2
8
C
8
D
24.
The maximum number of non-zero elements in an actuation sub-matrix is also 24.
As the biochip contains a 10
10 electrode array, the maximum percentage
of non-zero elements in actuation sub-matrices is 24 %. Therefore, we can find
that 24 % is the upper bound on the percentage of non-zero elements in the error
dictionary for the bioassay. It is important to note that, the above analyses can be
applied to the situation with any number of errors occurred in the bioassay. This
upper bound for the percentage of non-zero elements in an actuation sub-matrix is
independent with the number of errors occurred during the execution of bioassay.
Therefore, we have shown that, for exponential dilution bioassay, the actuation
matrices are sparse.
We can illustrate that actuation matrices are sparse in an alternative way. Accord-
ing to the fluidic constraints of biochip, in order to avoid droplet interferences, each
droplet has a guard-ring associated with it. Examples are as follows. Figure
3.4
a
shows the actuation electrodes for a droplet that stays on an electrode. When the
electrode under the droplet is actuated, all the other neighboring electrodes of the
droplet need to be deactivated.
a
Deactivated electrode
Activated electrode
Droplet
b
Deactivated electrode
Activated electrode
Droplet
Fig. 3.4
(
a
) The actuation signals applied on electrodes when a droplet stays at an electrode;
(
b
) the actuation signals applied on electrodes when a droplet is being moved from one electrode
